PARI/GP is free software,
covered by the GNU General Public License,
 and comes WITHOUT ANY WARRANTY WHATSOEVER.

parisize = 4000000, primelimit = 500000

? a = [ 6,3,-1; 3,2,0; -1,0,0]
%1 =
[ 6 3 -1]

[ 3 2  0]

[-1 0  0]

? b = [ -2,4,2;4,8,4;2,4,-2]
%2 =
[-2 4  2]

[ 4 8  4]

[ 2 4 -2]


? h = t * a - b
%8 =
[6*t + 2 3*t - 4 -t - 2]

[3*t - 4 2*t - 8     -4]

[ -t - 2      -4      2]


? d
%10 = d
? d = matdet(h)
%11 = -2*t^3 + 30*t^2 - 96*t - 128
? factor(d)
%12 =
[t - 8 2]

[t + 1 1]

?